It should fly : (regular) ornithopters are available as flying models, and a university has built and flown both human and engine-powered vehicles.

Like a helicopter, it has 2 or more wings attached to a hub ; unlike a regular helicopter where the hub pushes against the fuselage to turn, the wings push themselves... topographically like a tip-jet 'copter.

I really have no idea if this would fly or not. My gut is
saying no, an ornithopter needs to push against the wind to
generate thrust as well as lift; here the thrust simply spins
the blades faster. What lifting force that would otherwise
result seems lost. But I could be wrong.

Well, obviously the wings would be designed specifically for
the application. It's not difficult to imagine the outer
portions of the blade doing most of the work : like a
helicopter, the bit closest the axis doesn't do much: not
enough speed or room to work.

I'm sure that some configuration matching this description
could be made to fly. It would definitely be cool to watch.

I wonder if it might be useful on an extremely small scale. I
have the impression that it is much easier to create a
flapping motion with MEMS than to create a MEMS motor
coupled to a propeller. But pure flapping flight is pretty
tricky. By putting enough wings around a rigid ring, the
oscillations get canceled out.

There's possibly a solid airfoil that could be useful for the entire flap sequence, but I had in mind each blade having a few adjustable spars to cycle it through different airfoils for different AoA's - that and a cotton or clear-mylar skin would give it the required steampunky/DaVinci look.